研究迟滞微分系统稳定与控制的一种新方法  

A New Kind of Method to Research. of the Stability and Control of Delay Differential System

作　　者：伊丽娜[1] 包俊东[1] 套格图桑[1,2] YI Li-na1, BAO Jun-dong1, Taogetusang1,2(1. The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China ;2. The College of Mathematical, Inner Mongolia University for Nationalities, Tongliao 028043, Chin)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古民族大学数学学院,内蒙古通辽028043

出　　处：《数学的实践与认识》2018年第6期242-254,共13页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11361040);内蒙古自治区自然科学基金(2015MS0128);内蒙古自治区高等学校科学研究基金(NJZY16180);内蒙古自治区2016年硕士研究生科研创新项目(S20161013502);内蒙古民族大学科学研究基金资助项目(NMDGP1713)

摘　　要：基于李雅普诺夫判定稳定性两种方法，用一种三角函数型辅助方程及其相关结论，研究了一种迟滞微分系统的求解、稳定与控制问题．步骤一、给出一种三角函数型辅助方程的精确解．步骤二、通过三角函数变换与三角函数型辅助方程，将一种迟滞微分系统的求解问题转化为非线性代数方程组的求解问题．步骤三、借助符号计算系统Mathematica求出代数方程组的解，并构造了一种迟滞微分系统的精确解．步骤四、通过分析研究精确解，获得了一种迟滞微分系统的稳定与控制相关的几种结论．According to the two kinds of Lyapunov judging stability, by the relative conclu- sions of a kind of trigonometric function auxiliary equation, the problems of solving solutions, stability and control of a kind of delay differential system are researched. Step1, the accurate solutions of the trigonometric function type auxiliary equation are presented. Step2, by trigonometric function transformation and trigonometric function type auxiliary equation, the problem of solving solutions of a kind of delay differential system is changed to the problem of solving solutions of the nonlinear algebra equations. Step3, with the help of the symbol calculate system Mathematica, the solutions of the algebra equations are solved, and the accurate solutions of a kind of delay differential system are constructed. By researching the accurate solutions, some kinds of conclusions of the stability and the control of a kind of delay differential system are obtained.

关 键 词：一种迟滞微分系统 三角函数型辅助方程 符号计算系统Mathematica 稳 定与控制 

分 类 号：O175[理学—数学]